The transformer X2 look like it might be connected as a current transformer. Indeed, the narrator of the video identifies it as such. It’s just a regular transformer configured as a CT. It probably not a very linear CT but it will work. The output of the CT is rectified and smoothed to get a DC value proportional to the current. You need some transient protection on A0. Maybe a 5V Zener. There is no circuitry for voltage measurement. It appears that they are assuming a fixed mains voltage and a unity power factor. P=IV cos ϕ . The mains voltage and current are isolated by the two transformers. It won’t be very accurate but it's good enough for a demo. What is the +12V for? It looks like IC117 etc is mislabelled, does is provide 3.3V for another module, maybe Wi-Fi? Don’t forget to install fuses!
In a real life meter, you would measure the current, voltage, frequency and the time offset of the zero crossing points to determine the phase angle.
Take care.